Projection lens apparatus and projection type image display apparatus

ABSTRACT

Compactness of a projection type image display apparatus is realized by achieving miniaturization and wide-angle of a projection lens apparatus while various kinds of aberration are satisfactorily compensated. A first lens group having a negative refracting power, a second lens group having a positive refracting power, and a third lens group having a positive refracting power are positioned in this order, from a screen side, toward an image display element side, in the projection lens apparatus. When f, f 1 , f 3 , f 23 , and f b  represent, respectively, a focal length of the whole lens system, a focal length of the first lens group, a focal length of the third lens group, a combined focal length of the second and third lens groups, and a back focus of the whole lens system, the projection lens apparatus satisfies the following conditions:  
     1.4&lt;| f   1   |/f    (1)  
     2.8&lt; f   3   /f    (2)  
     3.6&lt; f   b   /f    (3)  
     0.1&lt;| f   1   /f   23  |&lt;0.3   (4)

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a projection lens apparatus for allowing a source light to be made incident in an image display apparatus so that an overhead projection of the reflected light or the transmitted light is performed on a projection screen, and also relates to a projection type image display apparatus equipped with the projection lens apparatus.

[0003] 2. Description of the Prior Art

[0004] The main stream of a projection type image display apparatus has been a type that performs an overhead projection of an image formed in a CRT. In order to improve the efficiency of light usage, and reduce the size and the weight of the apparatus, a projection type image display equipped with a liquid crystal display element and a micro mirror display element (hereinafter, referred to as a DMD element) instead of a CRT has been recently developed. This projection type image display apparatus is configured such that a source light is modulated by transmitting or reflecting it at each pixel in accordance with video signals applied to the above display element, thereby allowing a projection lens apparatus to perform a overhead projection and thus form an image.

[0005] Although the image display apparatus equipped with a CRT is capable of electrically compensating distortion aberration of a projection image, the image display apparatus equipped with a liquid crystal display element or a DMD element is not. For that reason, the latter apparatus is required to optically compensate the distortion aberration.

[0006] A projection type lens apparatus using liquid display elements also has been developed as set forth, e.g., in JP-A-11-149041 specification, however, it has a drawback of a short back focus of about 20 mm.

SUMMARY OF THE INVENTION

[0007] In view of the above problems, it is an object of the present invention to provide a projection lens apparatus for forming an image with high resolution by satisfactorily compensating various kinds of aberration, while securing an appropriate back focus so that another optical component is arranged between the projection lens apparatus and an image display element such as a liquid crystal display element and a DMD element.

[0008] In order to attain the above described object, a projection lens apparatus according to the present invention is designed to satisfy the following conditions (1) to (4), in which a first lens group having a negative refracting power, a second lens group having a positive refracting power, and a third lens group having a positive refracting power are arranged from a projection screen side (a light emission side) to an image display element side (a light incidence side) in this order.

1.4<|f ₁ |/f   (1)

2.8<f ₃ /f   (2)

3.6<f _(b) /f   (3)

0.1<|f ₁ /f ₂₃|<0.3   (4)

[0009] here, f, f₁, and f₃ represent focal lengths of a whole lens system, a first lens group, and a third lens group, respectively, and f₂₃ represents a combined focal length of a second and third lens groups, and further f_(b) represents a back focus of the whole lens system.

[0010] Power distribution of the first to third lens groups as defined above allows the projection lens apparatus to compensate satisfactorily various kinds of aberration, while the compactness and the wide-angle of the apparatus are achieved.

[0011] The conditions (1) and (2) are set to reduce chromatic aberration of magnification by controlling powers of the first and third lens groups which are to have a maximum off-axis ray height. It becomes difficult to compensate the chromatic aberration of magnification, when |f₁|/f and f₃/f become equal to or fall below the respectively corresponding lower limits.

[0012] The condition (3) is set to secure an appropriate back focus. When f_(b)/f becomes equal to or falls below its lower limit, the back focus becomes smaller, accordingly making it difficult to arrange an optical component between the lens apparatus and the liquid crystal image display such as the liquid crystal display element and the DMD element.

[0013] The condition (4) is set to secure an appropriate back focus and to reduce distortion aberration. When |f₁/f₂₃| becomes equal to or exceeds its upper limit, positive powers of the second and third lens groups increase, accordingly making it difficult to secure an appropriate back focus. On the other hand, a negative power of the first lens group increases, thereby causing negative distortion aberration to increase, when |f₁/f₂₃| becomes equal to or falls below its lower limit.

[0014] The projection lens apparatus according to the present invention also may allow the first, second and third lens groups to have aspherical surfaces. If every lens group has an aspherical surface thereat, the first and third lens groups compensate aberration such as distortion aberration and chromatic aberration of magnification on the aspherical surfaces thereof, and the second lens group compensates aberration of an on-axis ray on its aspherical surface. This configuration permits the lens apparatus to have more versatility of possible compensation of aberration, accordingly to perform further compensation of aberration.

[0015] In particular, using an aspherical surface as an emission surface of a third lens of the third lens group, having a large off-axis ray height, serves to effectively compensate aberration of an off-axis ray. Using an aspherical surface also as an incidence surface of a second lens of the second lens group serves to most effectively compensate aberration of an on-axis ray.

[0016] Using a plastic lens as a first lens of the first lens group, having a largest diameter among lenses of the projection lens apparatus according to the present invention, allows the apparatus according to the present invention to reduce its weight. However, since the plastic lens changes in shape according to changes in temperature and humidity, the lens characteristics thereof such as lens focus and MTF deteriorates, when the plastic lens has a large power. The condition below is intended to control the power of the plastic lens so that the lens characteristics do not deteriorate even when the plastic lens changes in shape according to changes in temperature and humidity.

7<|f _(L1) /f|  (5)

[0017] A typical plastic lens has poor accuracy in shape and large deviations in shape accuracy compared to a glass lens. To suppress the deterioration of the plastic lens having deviations in shape accuracy, a ray is made incident on the plastic lens, in a direction substantially perpendicular to the plastic lens, serving as the first lens of the first lens group in the projection lens apparatus according to the present invention. This configuration allows the plastic lens to have a larger tolerance in shape and enhance its manufacturability.

[0018] Achieving the compactness and the wide-angle of the projection lens apparatus is required to reduce the size of the project type image display apparatus. Decentering the optical axis of the lens apparatus against the center of the projection screen allows the projection type image display apparatus to be downsized further. Decentering the projection lens apparatus against the center of the projection screen requires decentering a Fresnel screen against the projection screen.

[0019] When the optical axis of the projection lens apparatus is decentered against the center of the projection screen, ratios of peripheral light quantities at the upper and lower parts of the screen are generally different because of different distances from the optical axis of the projection lens apparatus to the upper and lower parts of the screen. In the projection type image display apparatus according to the present invention, difference in ratios of peripheral light quantities at the upper and lower parts of the screen is designed to be 10% or less so that brightness at the upper and lower parts of the screen is substantially equal.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020]FIG. 1 is a schematic view of a projection lens apparatus according to a first embodiment of the present invention;

[0021]FIG. 2 is an illustration of spherical aberration of the projection lens apparatus according to the first embodiment;

[0022]FIG. 3 is an illustration of astigmatism of the projection lens apparatus according to the first embodiment;

[0023]FIG. 4 is an illustration of distortion aberration of the projection lens apparatus according to the first embodiment;

[0024]FIG. 5 is a schematic view of a projection lens apparatus according to a second embodiment of the present invention;

[0025]FIG. 6 is an illustration of spherical aberration of the projection lens apparatus according to the second embodiment;

[0026]FIG. 7 is an illustration of astigmatism of the projection lens apparatus according to the second embodiment;

[0027]FIG. 8 is an illustration of distortion aberration of the projection lens apparatus according to the second embodiment;

[0028]FIG. 9 is a schematic view of a projection lens apparatus according to a third embodiment of the present invention;

[0029]FIG. 10 is an illustration of spherical aberration of the projection lens apparatus according to the third embodiment;

[0030]FIG. 11 is an illustration of astigmatism of the projection lens apparatus according to the third embodiment;

[0031]FIG. 12 is an illustration of distortion aberration of the projection lens apparatus according to the third embodiment;

[0032]FIG. 13 is a schematic view of a projection lens apparatus according to a fourth embodiment of the present invention;

[0033]FIG. 14 is an illustration of spherical aberration of the projection lens apparatus according to the fourth embodiment;

[0034]FIG. 15 is an illustration of astigmatism of the projection lens apparatus according to the fourth embodiment;

[0035]FIG. 16 is an illustration of distortion aberration of the projection lens apparatus according to the fourth embodiment;

[0036]FIG. 17 is a schematic view of a projection lens apparatus according to a fifth embodiment of the present invention;

[0037]FIG. 18 is an illustration of spherical aberration of the projection lens apparatus according to the fifth embodiment;

[0038]FIG. 19 is an illustration of astigmatism of the projection lens apparatus according to the fifth embodiment;

[0039]FIG. 20 is an illustration of distortion aberration of the projection lens apparatus according to the fifth embodiment;

[0040]FIG. 21 is a schematic view of a projection type image display apparatus in which there is incorporated the projection lens apparatus according to any one of the above embodiments; and

[0041]FIG. 22 is an illustration of a vignetting factor of the projection lens apparatus according to any one of the above embodiments.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0042] Referring now to the attached drawings, preferred embodiments of the present invention will be described. FIGS. 1, 5, 9, 13, and 17 are illustrations of projection lens apparatuses according to the embodiments of the present invention. The following description will be focused mainly on FIG. 1, and descriptions on FIGS. 5, 9, 13, and 17 will be omitted since these figures are considered to be understood from data in Tables 2 to 5 and on the analogy of the description on FIG. 1.

[0043]FIG. 1 is a schematic view of a first embodiment of the projection lens apparatus and its associated optical components showing, from a projection screen (not shown) or the left side of the plane of the figure, a first lens group 1, a second lens group 2, a third lens group 3, a total reflection prism (hereinafter, referred to as a TIR prism) 5, and a DMD element 6 in this order. The above three lens groups 1 to 3 constitute a projection lens apparatus 4. A ray emitted from a light source is made incident on an incidence plane 51 of the TIR prism 5, and is totally reflected at a total reflection plane 52 of the TIR prism 5, and then is made incident on the DMD element 6. After reflected on an active plane of the DMD element 6, the incident ray transmits the TIR prism 5, and is made incident on the projection lens apparatus 4, and then is projected on the screen.

[0044] The projection lens apparatus 4 is provided with the first lens group 1 having a negative refracting power, the second lens groups 2 having a positive refracting power, and third lens groups 3 having a positive refracting power. The first lens group 1 includes a first lens 11 as well as a second lens 12 of negative meniscus lenses facing their convex surfaces toward the screen, and a third lens 13 of a biconcave lens, in addition to a fourth lens 14 of a biconvex lens. The second lens group 2 includes a fifth lens 21 of a biconvex lens, an aperture 22, and a sixth lens 23 of a biconvex lens. The third lens group 3 includes a seventh lens 31 and an eighth lens 32 having a mating face therebetween, a ninth lens 33 facing its concave surface toward the screen, and a tenth lens 34 of a biconvex lens.

[0045] In the first embodiment shown in FIG. 1, a resin is bonded on one surface of each of the sixth lens 23 of the second lens group 2 and the ninth lens 33 of the third lens group 3 (hereinafter, these lenses are referred to as hybrid lenses). While the resin-bonded surface of each of the hybrid lenses is spherical, the opposite surface thereof is aspherical. The first lens 11 of the first lens group 1 is made from plastic and the largest in diameter among the lenses in the projection lens apparatus 4. Using a plastic lens as the first lens 11 serves to reduce the weight of the projection lens apparatus 4. The plastic lens, however, has a problem such that the lens changes in shape according to changes in temperature and humidity, thereby causing deterioration of its lens characteristics. Controlling a power of the plastic lens is required to suppress the deterioration of the lens characteristics due to temperature and humidity. To minimize the deterioration of the lens characteristics, the present invention sets the following condition:

7<|f _(L1) /f |

[0046] here,

[0047] f: a focal length of the whole lens system; and

[0048] F_(L1): a focal length of the first lens 11 of the first lens group 1.

[0049] The plastic lens has generally poor accuracy in shape compared to a glass lens. To suppress the deterioration of the lens with poor accuracy in shape, a ray is made incident on the first lens 11 in a direction substantially perpendicular to the first lens 11 of the first lens group 1 in the projection lens apparatus 4 according to the present invention. This configuration allows the plastic lens to have a larger tolerance in shape and enhance its manufacturability. The plastic lens has aspherical surfaces, thereby serving to compensate distortion aberration.

[0050] The ninth lens 33 of the third lens group 3 is a hybrid lens having an aspherical surface. This serves to compensate off-axis aberration effectively because of a large off-axis ray height of the hybrid lens. The sixth lens 23 of the second lens group 2 arranged close to the aperture 22 is also a hybrid lens having an aspherical surface, thereby serving to compensate on-axis aberration effectively. With this configuration, a desired back focus is secured so that the TIR prism 5 is arranged between the projection lens apparatus 4 and the DMD element 6. Consequently, the projection lens apparatus 4 is allowed to compensate various kinds of aberration satisfactorily and realize performing a high-resolution projection, while achieving its miniaturization and wide-angle. In order to realize these states, it is required to meet the following conditions:

1.4<|f ₁ |/f   (1)

2.8<f ₃ /f   (2)

3.6<f _(b) /f   (3)

0.1<|f ₁ /f ₂₃|0.3   (4)

[0051] here,

[0052] f: a focal length of the whole lens system;

[0053] f_(b): a back focus of the whole lens system;

[0054] f₁: a focal length of the first lens group;

[0055] f₃: a focal length of the third lens group; and

[0056] f₂₃: a combined focal length of the second and third lens groups.

[0057] The conditions (1) and (2) are set to reduce chromatic aberration of magnification by controlling the powers of the first and third lens groups having a maximum off-ray height. It becomes difficult to compensate the chromatic aberration of magnification, when |f₁|/f and f₃/f become equal to or fall below the respectively corresponding lower limits.

[0058] The condition (3) is set to secure an appropriate back focus. The back focus becomes shorter, when f_(b)/f becomes equal to or falls below its lower limit. In this case, there is insufficient space left between the projection lens apparatus and a liquid crystal display element or the DMD element in which an optical element is arranged.

[0059] The condition (4) is set to secure the appropriate back focus and reduce negative distortion aberration. When |f₁/f₂₃| becomes equal to or exceeds its upper limit, the positive powers of the second and third lens groups become larger, thereby leading to difficulty in securing the appropriate back focus. When |f₁/f₂₃| becomes equal to or falls below its lower limit, the negative power of the first lens group becomes larger, thereby leading to increase in negative distortion aberration.

[0060] Referring now to the attached tables, the embodiments of the present invention will be described in further detail. Table 1 corresponds to FIG. 1, which is a schematic view of the projection lens apparatus according to the first embodiment of the present invention. Similarly, Tables 2, 3, 4, and 5 correspond to FIGS. 5, 9, 13, and 17, respectively. In these tables, R_(i) represents a radius of curvature of an ith surface counted from the screen including the surface of the aperture. D_(i) represents a distance, on the optical axis, from the ith to (i+1)th surfaces counted from the screen. N_(j) and v_(j) represent a refractive index and an Abbe number (d line) of the jth lens counted from the screen.

[0061] When R_(i), K, h, and A, B, C, D, etc., are given, a shape of an aspherical surface is specified in the following widely used equation: $Z = {\left( {1/R_{i}} \right) \cdot {\quad{h^{2}/\left\lbrack {1 + \quad \sqrt{\left. \left\{ {1 - {\left( {K + 1} \right) \cdot \left( {1/R_{i}} \right)^{2} \cdot h^{2}}} \right\} \right\rbrack + {A \cdot h^{4}} + {B \cdot h^{6}} + {C \cdot h^{8}} + {D \cdot h^{10}} + \ldots}} \right.}}}$

[0062] here,

[0063] Z: an axis in the optical axis;

[0064] R_(i): a radius of curvature of an ith surface on the optical axis;

[0065] K: a conical constant;

[0066] h: an axis in the radium direction of a lens; and

[0067] A, B, C, D, etc.: high order coefficients of the aspherical surface. TABLE 1 i j R_(i) D_(i) N_(i) ν_(j)  1 1 56.822 5 1.499091 58.0  2 24.186 12.13  3 2 59.369 2 1.62041 60.3  4 21.691 12.58  5 3 −32.19 2 1.74400 44.9  6 31.969 4.46  7 4 298.82 4.99 0.84666 23.8  8 −50.963 0.52  9 5 31.151 7.49 1.65412 39.6 10 −144.61 23.39 11 ∞ 7.6 (aperture) 12 6 −526.002 0.1 1.520200 52.0 13 7 5513.648 4.84 1.49700 81.6 14 −12.03 0.5 15 8 −12.099 2 1.75520 27.5 16 9 25.096 6.93 1.49700 81.6 17 −24.778 0.51 18 10  −85.7 5.52 1.49700 81.6 19 11  −23.628 0.1 1.520200 52.0 20 −26.797 0.5 21 12  186 6.04 1.84666 23.8 22 −39.674 5 23 13  ∞ 27 1.51680 64.2 24 ∞ 4.5 25 14  ∞ 2.75 1.47200 55 26 ∞ 1.55

[0068] Aspherical surface:

[0069] 1st surface K: 2.068172, A: −9.034348e−7,

[0070] B: 2.140360e−9, C: −1.175769e−12,

[0071] D: 2.708077e−16

[0072] 2nd surface K: −1.161402, A: −4.055402e−7,

[0073] B: −5.42700e−10, C: 8.850174e−12,

[0074] D: −1.234473e−14

[0075] 12th surface K: −6729.736862, A: −4.477155e−5,

[0076] B: −1.779039e−7, C: 1.971636e−9,

[0077] D: −1.147868e−11

[0078] 20th surface K: 1.456989, A: 4.909620E−6,

[0079] B: 2.770520e−9, C: 2.103590e−11,

[0080] D: 3.609500e−14

[0081] F-number: FNO=2.75half field angle: ω=43.9°

[0082] f: 11.28, f_(b): 40.8, f₁: −17.1, f₃: 48.7, f₂₃: 81.5

|f ₁ |/f =1.52

f ₃ /f =4.3

f _(b) /f =3.62

|f ₁ /f ₂₃|=0.21

|f _(L1) /f|=7.98

[0083] Spherical aberration, astigmatism, and distortion aberration related to Table 1 are shown in FIGS. 2, 3, and 4, respectively. In these figures, G, R, and B indicate aberration of the wavelengths of rays of 555 nm, 650 nm, and 450 nm, respectively. S and M indicate, respectively, a sagittal image surface and a meridional image surface of a wavelength of a ray of 555 nm. FIGS. 2 to 4 apparently indicate that the aberration shown in the above figures are satisfactorily compensated, accordingly realizing lens characteristics of the projection lens apparatus necessary for high image quality. Although a DMD element is employed as an image display element in the above-described embodiment, a liquid crystal display element or a display element, which transmits and reflects rays for forming an image by using electrical signals, may be employed instead of the DMD element. TABLE 2 i j R_(i) D_(i) N_(i) ν_(j)  1 1 100 3.3 1.490901 58.0  2 27.973 8.72  3 2 53.502 2 1.62041 60.3  4 24.705 11.81  5 3 411049.78 4 1.49091 58.0  6 22.355 15.77  7 4 36.502 4.67 1.84666 23.8  8 −5528.298 19.79  9 ∞ 6.8 (aperture) 10 5 −2031.293 3.01 1.48749 70.4 11 −27.791 2.765 12 6 −18.102 2 1.80518 25.5 13 7 36.397 5 1.48749 70.4 14 −40.088 1 15 8 352.742 4.48 1.48749 70.4 16 −38.889 1 17 9 71.023 7.04 1.58144 40.9 18 −39.912 1 19 10  425.704 5.06 1.49091 58.0 20 −43.288 5 21 11  ∞ 27 1.51680 64.2 22 ∞ 4.5 23 12  ∞ 2.75 1.47200 55.0 24 ∞ 1.55

[0084] Aspherical surface:

[0085] 1st surface K: 0, A: 1.303107Ee−3, B: 1.54150e−6,

[0086] C: 1.185250e−9, D: −5.127177e−13

[0087] 2nd surface K:0, A:5.820000e-4, B: 2.944327e-7,

[0088] C: −4.041408e−9, D: −3.178235e−13

[0089] 5th surface K: −683119333.312, A: 7.560320e−4,

[0090] B: −9.918486e−6, C: 4.248327e−8,

[0091] D: −7.666378e−11

[0092] 6th surface K: −1.907139, A: 1.750551e−3,

[0093] B: −2.284930e−5, C: 1.382748e−7,

[0094] D: −2.934505e−10

[0095] 19th surface K: 0, A: −5.439591e−4, B: −3.067743e−6,

[0096] C: 1.206313e−8, D: 6.496498e−12

[0097] 20th surface K: 0, A: 3.892849e−4, B: −3.091477e−6,

[0098] C: 1.131288e−8, D: 1.049618e−11

[0099] F-number: FNO=2.75 half field angle: ω=43.9°

[0100] f: 11.23, f_(b:) 40.8, f₁: −16.6, f₃ 33.3, f₂₃: 59.1

|f ₁ |/f=1.48

f ₃ /f=2.97

f _(b) /f=3.62

|f ₁ /f ₂₃|=0.288

|f _(L1) /f|=7.12

[0101] Spherical aberration, astigmatism, and distortion aberration related to Table 2 are shown in FIGS. 6, 7, and 8, respectively. In these figures, G, R, and B indicate aberration of the wavelengths of rays of 555 nm, 650 nm, and 450 nm, respectively. S and M indicate, respectively, a sagittal image surface and a meridional image surface of a wavelength of a ray of 555 nm.

[0102] FIGS. 6 to 8 apparently indicate that the aberration shown in the above figures are satisfactorily compensated, accordingly realizing lens characteristics of the projection lens apparatus necessary for high image quality. TABLE 3 i j R_(i) D_(i) N_(i) ν_(j)  1 1 60.605 5 1.499091 58.0  2 24.903 6.5  3 2 43.695 2 1.62041 60.3  4 19.327 15.35  5 3 −36.121 2 1.74400 44.9  6 31.698 4.52  7 4 135.746 5.1 0.84666 23.8  8 −64.108 0.5  9 5 31.252 7.97 1.65412 39.6 10 −194.4 26.06 11 ∞ 7 (aperture) 12 6 −273.905 0.1 1.520200 52.0 13 7 −280.909 4.66 1.49700 81.6 14 −12.338 0.5 15 8 −12.754 2 1.75520 27.5 16 9 23.486 6.87 1.49700 81.6 17 −25.81 0.5 18 10  −78.468 6.04 1.49700 81.6 19 11  −21.737 0.1 1.520200 52.0 20 −24.296 0.5 21 12  470.507 5.93 1.84666 23.8 22 −36.23 5 23 13  ∞ 27 1.51680 64.2 24 ∞ 4.5 25 14  ∞ 2.75 1.47200 55 26 ∞ 1.55

[0103] Aspherical surface:

[0104] 1st surface K: 2.429735, A: 1.883753e−6,

[0105] B: −3.060454e−9, C: 2.691520e−12,

[0106] D: −1.704096e−15

[0107] 2nd surface K: −1.097959, A: −5.144892e−7,

[0108] B: −8.354796e−9, C: −3.030524e−12,

[0109] D: 8.085546e−15

[0110] 12th surface K: −6006.527896, A: −9.250468e−5,

[0111] B: 5.790455e−7, C: −1.088606e−8,

[0112] D: 6.718634e−11

[0113] 20th surface K: 1.170151, A: 5.679944E−6,

[0114] B: 8.160707e−9, C: 8.28354e−12,

[0115] D: 1.159747e−13

[0116] F-number: FNO=2.75 half field angle: ω=43.9°

[0117] f: 11.25, f_(b): 40.8, f₁: −18.1, f₃: 43.68, f₂₃: 93.15

|f ₁ |/f=1.61

f ₃ /f=3.88

f _(b) /f=3.62

|f ₁ f ₂₃|=0.19

|f _(L1) /f|=8

[0118] Spherical aberration, astigmatism, and distortion aberration based on Table 3 are shown in FIGS. 10, 11, and 12, respectively. In these figures, G, R, and B indicate aberration of the wavelengths of rays of 555 nm, 650 nm, and 450 nm, respectively. S and M indicate, respectively, a sagittal image surface and a meridional image surface of a wavelength of a ray of 555 nm. FIGS. 10 to 12 apparently indicate that the aberration shown in the above figures are satisfactorily compensated, accordingly realizing lens characteristics of the projection lens apparatus necessary for high image quality. TABLE 4 i j R_(i) D_(i) N_(i) ν_(j)  1 1 55.203 5 1.499091 58.0  2 23.856 67.977  3 2 51.569 2 1.62041 60.3  4 20.953 14.07  5 3 −33.488 2 1.74400 44.9  6 31.698 4.65  7 4 242.91 5.5 0.84666 23.8  8 −56.232 0.52  9 5 32.267 7.9 1.65412 39.6 10 −135.746 24.87 11 ∞ 7.5 (aperture) 12 6 −1072.605 0.1 1.520200 52.0 13 7 5513.648 4.69 1.49700 81.6 14 −12.467 0.5 15 8 −12.562 2 1.75520 27.5 16 9 24.265 7.07 1.49700 81.6 17 −24.809 0.5 18 10  −75.256 5.66 1.49700 81.6 19 11  −22.694 0.1 1.520200 52.0 20 −25.996 0.5 21 12  370.391 6.07 1.84666 23.8 22 −36.397 5 23 13  ∞ 27 1.51680 64.2 24 ∞ 4.5 25 14  ∞ 2.75 1.47200 55 26 ∞ 1.55

[0119] Aspherical surface:

[0120] 1st surface K: 2.068171, A: 3.704251e−7,

[0121] B: −1.773038e−9, C: 2.586699e−12,

[0122] D: −1.350369e−15

[0123] 2nd surface K: −1.080023, A: −3.950647e−7,

[0124] B: −1.071853e−8, C: 1.462552e−11,

[0125] D: −1.035022e−14

[0126] 12th surface K: −6729.726862, A: −4.546386e−5,

[0127] B: −1.908974e−7, C: 2.662512e−9,

[0128] D: −2.171104e−11

[0129] 20th surface K: 1.349085, A: 6.028083E−6,

[0130] B: 5.573375e−9, C: 1.681841e−11,

[0131] D: 5.542812e−14

[0132] F-number: FNO=2.75 half field angle: ω=43.9°

[0133] f: 11.2578, f_(b): 40.8, f₁: −17.42, f₃: 46.14, f₂₃: 90.02

|f ₁ /f=1.55

f ₃ /f=4.10

f _(b) /f=3.62

|f ₁ /f ₂₃|=0.12

|f _(L1) /f|=7.99

[0134] Spherical aberration, astigmatism, and distortion aberration based on Table 4 are shown in FIGS. 14, 15, and 16, respectively. In these figures, G, R, and B indicate aberration of the wavelengths of rays of 555 nm, 650 nm, and 450 nm, respectively. S and M indicate, respectively, a sagittal image surface and a meridional image surface of a wavelength of a ray of 555 nm. FIGS. 14 to 16 apparently indicate that the aberration shown in the above figures are satisfactorily compensated, accordingly realizing lens characteristics of the projection lens apparatus necessary for high image quality. TABLE 5 i j R_(i) D_(i) N_(i) ν_(j)  1 1 99.901 5 1.490901 58.0  2 27.806 5.99  3 2 36.686 2 1.62041 60.3  4 23.142 14.769  5 3 147.145 4.2 1.49091 58.0  6 15.898 17.55  7 4 37.324 4.504 1.84666 23.8  8 −338.388 16.5  9 ∞ 6.022 (aperture) 10 5 148.210 2.88 1.48749 70.4 11 −35.173 2.733 12 6 −20.098 2 1.80518 25.5 13 7 23.125 5.217 1.48749 70.4 14 −38.451 1.550 15 8 581.969 4.085 1.48749 70.4 16 −44.686 1 17 9 115.239 7.073 1.58144 40.9 18 −30.898 1 19 10  −1723.784 5.117 1.49091 58.0 20 −38.589 5 21 11  ∞ 27 1.51680 64.2 22 ∞ 4.5 23 12  ∞ 2.75 1.47200 55.0 24 ∞ 1.55

[0135] Aspherical surface:

[0136] 1st surface K: −26.973907, A: 1.268671Ee−5,

[0137] B: −1.401240e−8, C: 9.599903e−12,

[0138] D: −3.473665e−15

[0139] 2nd surface K: −0.043044, A: 6.080164e−5,

[0140] B: 1.133503e−9, C: −3.810279e−11,

[0141] D: 7.928239e−17

[0142] 5th surface K: −106.491112, A: 4.681539e−6,

[0143] B: −1.235157e−7, C: 4.670941e−10,

[0144] D: −7.569594e−13

[0145] 6th surface K: −719376, A: 4.522386e−6,

[0146] B: −2.621143e−7, C: 1.498970e-−b 9,

[0147] D: −3.115547e−12

[0148] 19th surface K: 8181.539060, A: −1.735505e−5,

[0149] B: −3.594589e−8, C: 3.445454e−12,

[0150] D: −7.173390e−14

[0151] 20th surface K: 1.780692, A: −5.749135e−6,

[0152] B: −3.207989e−8, C: 3.733309e−11,

[0153] D: −9.642571e−14

[0154] F-number: FNO=2.75 half field angle: ω=43.9°

[0155] f: 11.257, f_(b): 40.8, f₁: −15.94, f₃: 32.6, f₂₃: 53.95

|f ₁ |/f=1.42

f ₃ /f=2.89

f _(b) /f=3.62

|f ₁ /f ₂₃|=0.295

|f _(L1) /f|=7.10

[0156] Spherical aberration, astigmatism, and distortion aberration based on Table 5 are shown in FIGS. 18, 19, and 20, respectively. In these figures, G, R, and B indicate aberration of the wavelengths of rays of 555 nm, 650 nm, and 450 nm, respectively. S and M indicate, respectively, a sagittal image surface and a meridional image surface of a wavelength of a ray of 555 nm. FIGS. 18 to 20 apparently indicate that the aberration shown in the above figures are satisfactorily compensated, accordingly realizing lens characteristics of the projection lens apparatus necessary for high image quality.

[0157]FIG. 21 is a schematic view of a projection type image display apparatus equipped with the projection lens apparatus according to any of the embodiments of the present invention. A light emitted from a light source is made incident on the DMD element 6, and then a light reflected thereat is made incident on the projection lens apparatus 4. The incident light is emitted at the projection lens apparatus 4, and reflected at a mirror 7. Thus, an overhead projection of an image formed at the DMD element 6 is performed on the projection screen 8. The mirror 7 is intended to bend the light path of the light emitted at the projection lens apparatus 4 so as to reduce the size of the projection type image display apparatus 9. Additionally, the miniaturization and wide-angle of the projection lens apparatus 4 serves to reduce the size of the projection type image display apparatus 9.

[0158] Decentering the optical axis of the projection lens apparatus 4 against the center of the screen 8 allows each component in the projection type image display apparatus 9 to be arranged in an optimal manner, thereby achieving further miniaturization of the projection type image display apparatus 9. In addition, this decentration accompanies making the center of a Fresnel screen to be decentered.

[0159]FIG. 22 shows vignetting factor vs. distance from the center of the projection screen. FIG. 22 indicates that, since the projection lens apparatus 4 has a high vignetting factor, the projection lens apparatus 4 used for the projection type image display apparatus 9 serves to form a bright image, favorably comparable with the one on the center of the screen, even on the periphery of the screen. Decentering the optical axis of the projection lens apparatus 4 against the center of the screen 8 as described above generally causes the projection lens apparatus 4 to have a vignetting factor different from the one, respectively, at the upper and lower parts of the screen, because of different object heights from the optical axis of the projection lens apparatus 4. This leads to different ratios of peripheral light quantities at the upper and lower parts of the screen, consequently ending up luminance unevenness on the screen. On the other hand, the projection lens apparatus according to any of the embodiments of the present invention has object heights of 0.9 and 1.0, respectively, at the upper and lower parts of the screen and this difference is about 8%. The small difference in these two object heights serves to have substantially equal ratios of peripheral light quantities on the whole screen, thus to obtain uniform brightness on the screen without luminance unevenness on the upper and lower parts of the screen.

[0160] As apparent from the drawings illustrating the lens characteristics, the projection lens apparatus according to the present invention satisfactorily compensates various kinds of aberration, while the compactness and the back focus of the projection lens apparatus are achieved. That is, the projection type image display apparatus equipped with the projection lens apparatus according to the present invention offers an image with high resolution, which is uniformly bright even on the periphery of the screen. 

What is claimed is:
 1. A projection lens apparatus for performing overhead projection of a ray modulated by an image display element on a projection screen, wherein there are positioned: a first lens group having a negative refracting power arranged closest to the screen; a second lens group having a positive refracting power arranged second closest to the screen; and a third lens group having a positive refracting power arranged between said second lens group and the image display element, and the projection lens apparatus satisfies the following conditions: 1.4<|f ₁ |/f 2.8<f ₃ /f where, f is a focal length of a whole lens system of the projection lens apparatus, and f₁ is a focal length of said first lens group, and also f₃ is a focal length of said third lens group.
 2. The projection lens apparatus according to claim 1, wherein the lens apparatus further satisfies the following condition: 3.6<f _(b) /f where, f_(b) is a back focus of the whole lens system of the projection lens apparatus.
 3. The projection lens apparatus according to claim 1 or 2, wherein the lens apparatus still further satisfies the further additional condition: 0.1<|f ₁ /f ₂₃|<0.3 where, f₂₃ is a combined focal length of said second lens group and said third lens group.
 4. The projection lens apparatus according to claim 1, 2 or 3, wherein said first lens group includes a first lens element made of plastic satisfying the condition: 7<|f _(L1) /f| where, f_(L1)is a focal length of the first lens element of said first lens group.
 5. The projection lens apparatus according to claim 4, wherein a ray emitted from the image display element is made incident on the first lens element in a direction substantially perpendicular to the first lens element.
 6. The projection lens apparatus according to claim 1, 2 or 3, wherein said second lens group includes a second lens element having an aspherical surface facing toward the screen.
 7. The projection lens apparatus according to claim 1, 2 or 3, wherein said third lens group includes a third lens element having an aspherical surface facing toward the image display element.
 8. The projection lens apparatus according to claim 1, 2 or 3, wherein said first lens group includes at least one aspherical surface.
 9. The projection lens apparatus according to claim 8, wherein said second lens group includes at least one aspherical surface.
 10. The projection lens apparatus according to claim 8 or 9, wherein said third lens group includes at least one aspherical surface.
 11. A projection type image display apparatus, further comprising the projection lens apparatus according to claim 1, 2 or
 3. 12. The projection type image display apparatus according to claim 11, wherein an optical axis of the projection lens apparatus is decentered from an center of the projection screen.
 13. The projection type image display according to claim 12, wherein the screen has, at least, a Fresnel screen, in such a manner that a center of the Fresnel screen is decentered from the center of the projection screen.
 14. The projection type image display according to claim 12, wherein difference in ratios of peripheral light quantities on upper and lower parts of the projection screen is 10% or less. 